Synthesis of Transformerless ActiveN-Port Networks

Abstract

Theorem: An arbitrary symmetric N × N matrix of real rational functions in the complex-frequency variable (a) can be realized as the immittance matrix of an N-port network containing only resistors, capacitors, and N negative-RC impedances, and (b) cannot, in general, be realized as the immittance matrix of an N-port network containing resistors, capacitors, inductors, ideal transformers, and M negative-RC impedances if M < N. The necessary and sufficient conditions for the immittance-matrix realization of transformerless networks of capacitors, self-inductors, resistors, and negative resistors follow as a special case of the theorem. In addition, an earlier result is extended by presenting a procedure for the realization of an arbitrary N × N short-circuit admittance matrix as an unbalanced transformerless active RC network requiring no more than N controlled sources. The passive RC structure has the interesting property that it can always be realized as a (3 N + 1)-terminal network of two-terminal impedances with common reference node and no internal nodes. The active subnetwork can always be realized with N negative-impedance converters.